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A novel method for measuring the thermal conductivity of organisms
ARTICLE IN PRESS Journal of Thermal Biology 34 (2009) 232–236
Contents lists available at ScienceDirect
Journal of Thermal Biology journal homepage: www.elsevier.com/locate/jtherbio
A novel method for measuring the thermal conductivity of organisms Kai Zhu, Ya-bo Wang , Ai Yang College of Mechanical Engineering, Tianjin University of Commerce, Tianjin 300134, China
a r t i c l e in f o
a b s t r a c t
Article history: Received 15 October 2008 Accepted 18 February 2009
Based on the theories of tissue optics and artificial neural network, the relationship between the optical properties and biological parameters was studied, and a new experimental method was derived. The properties of the organism were obtained indirectly by a black-box model derived by self-study of the artificial neural network between optical parameters and thermo-physical properties without using the heat transfer equation. In this method, the energy of light in diffuse radiation, diffuse transmission and collimated transmission was absorbed by a dual-integrating sphere experimental system of a spectrometer, and the spectrogram of the energy was obtained. Combining these spectral data of the energy, the diffuse-reflecting power, the diffuse transmissivity and the collimated transmissivity were calculated. The calculated results were taken as the input parameters of a black-box model. The experimental results show that there are apparent differences between the spectrogram of the energy on the diffuse radiation, the diffuse transmission and the collimated transmission of different matters, while there is a little difference in the same matter. Each spectrogram has its own characteristic. The values of the four thermal properties including the density, the constant pressure specific heat, the thermal diffusivity and the viscosity were calculated using the black-box model. Compared with the real values the calculated one has an average relative error between 5% and 5%. The conductivity of the tongue is 0.68 W/(m K) that calculated from the value of the density, the constant pressure specific heat and the thermal diffusivity. The results also show that there is a little difference on the conductivities in the longitudinal cross-section and the transverse section, but the effect of temperature on the conductivity of the tongue is not apparent. The difference implies the anisotropy of the properties of the organism, which cannot be easily obtained by a conventional experimental method. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Properties Bio-heat transfer Bio-optics Artificial neural network
1. Introduction Because of the complex structures with blood circulation, the thermal properties of the organism are different from those of inert materials, which vary with their type, structure and temperature. Therefore, the precise measurement of thermal properties in a biological tissue has become an important part of the study in biological technology. The aim of this paper is to study the relationship between the optical parameters and the biological properties, which are based on the distribution characteristic of optic radiation energy in the organism under a special condition. There are some reports about the application of optical theories in the study of thermal conductivity (Chia-Wei et al., 2001; Hatta and Sasuga, 1985; He, 2005). It was found in some turbid substances, such as polystyrene, milk or blood, that their characteristics of absorption and scattering are relatively stable. This is similar to the optical properties of organisms (Jackson et al., 1981; Han, 2003, 2005; Firbank and Delpy, 1993; Randall,
Corresponding author. Tel: +86 13512014043.
E-mail address: [email protected] (Y.-b. Wang). 0306-4565/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jtherbio.2009.02.007
1983). Based on this, the transferring rules and characteristics of light in organisms were studied to find the relationship between the nature parameters of the light and the properties of the organism. The optical parameters are used to describe the interaction between the optic, and the media is used to embody the micro-characteristics of materials. The complex interaction between light and organism tissue can be summed up as thermal effects, mechanical effects, photochemical effects, electromagnetic fields effect and biological effects. In this paper, the proposed method to simulate the distributing characteristics of light in organism tissues is based on determining the nature parameters such as the absorption coefficient, scattering coefficient and anisotropic factor with the analytic theory and the numerical theory. Compared with the traditional method, there are some advantages to the proposed method:
(1) The proposed method is fit for the materials with different structure and bioactivity such as organic tissues whilst the traditional methods are used to measure inert materials. (2) Instead of adopting the conventional heat transfer equation, the proposed method is used to obtain the optical parameters
ARTICLE IN PRESS K. Zhu et al. / Journal of Thermal Biology 34 (2009) 232–236
Nomenclature
a Cp Icr Ics Irr
Irs Itr
Its Rd Rdr Tcr Tdr Tc Td
thermal diffusivity, m2/s constant pressure specific heat, J/(kg K) energy of light received by detector 3, due to air contact with a dual-integrating sphere, W/m2 energy of light received by detector 3, due to sample contact with a dual-integrating sphere, W/m2 energy of light received by detector 1, due to standard reflective board contact with a dual-integrating sphere, W/m2 energy of light received by detector 1, due to sample contact with a dual-integrating sphere, W/m2 energy of light received by detector 2, due to standard reflective board posted to contact the second integrated sphere, W/m2 energy of light received by detector 2, due to sample contact with a dual-integrating sphere, W/m2 total diffuse reflectance diffuse reflectance of standard reflective board collimated transmittance of air diffuse transmittance of air total collimated transmittance total diffuse transmittance
233
Greek symbols
a, b, g
empirical constant
Empirical constant
l
ma ms n r g
mean thermal conductivity, W m1 K1 absorption coefficient, m2/s dissipation coefficient, m2/s viscosity, Pa s density, kg/m3 anisotropy factor
Subscripts a c cal d exp eq fig s
air, absorption coefficient collimated transmittance calculated diffuse reflectance, diffuse transmittance experimental equation figure sample, scatter coefficient
of organisms by a black-box model from the nonlinear mapping between the nature parameters of light and the thermal properties of the organism. (3) The proposed method does not require detailed knowledge of the mechanism.
of error during the process, an extinction long tube and an attenuating medium were applied in the experiment. When measuring, some parameters such as the total diffuse reflectance Rd, total diffuse transmittance Td, and the total collimated transmittance Tc can be obtained as follows (symbols not consistent with equations):
2. Optic experiments of tissues
Rd ¼
Irs R Irr ds
(1)
Td ¼
Its T Itr dr
(2)
Tc ¼
Ics T cr Icr
(3)
2.1. Measuring system The schematic (Han, 2003) of the dual-integrating sphere experimental system of the spectrometer is shown in Fig. 1. As shown in the figure, the tested object was arranged between the dual-integrating spheres. The near-infrared light emitted by FT-IR spectroscopy irradiates to the dual-integrating spheres through reflector plate and lens. Schematic of the dual-integrating sphere experimental system of spectrometer diffuse radiation, diffuse transmission and the collimated transmission of the tested object were received by InGaAs detectors 1, 2 and 3, respectively. Then the spectrogram of the energy was obtained by a computer connected to the experimental system. To apply the ‘‘Adding Double’’ to the experiment, it is necessary to determine the entrance direction vertically to the measured object. In addition, the size of spot on the tested material caused by the light is less than 10% of the integral sphere window filed. To reduce the effect
It is necessary to determine Rd, Td and Tc first. They are the foundation of calculating thermal properties. 2.2. Preparation of experimental materials In order to get the measured parameters, 30 samples were selected and are shown in Table 1. Because these samples were used as a reference, their relative parameters were known to verify the reliability and rationality of the nonlinear mapping between the nature parameters of the light and the thermal properties of the organism. In addition, to characterize the thermal performance of solid objects, it is necessary to determine the light transmittance of sliced materials. 2.3. Experimental design
Fig. 1. The dual-integrating sphere experimental system of the spectrometer.
Rd, Td, Tc given by Eqs. (1)–(3) are the input data to the blackbox model, and the computation of these parameters usually involves a tedious mathematical process, which requires the determination of the spectrogram of the energy in a dualintegrating sphere experimental system of a spectrometer. In order to obtain the correct value, the test is iterated by using the above selected objects.
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Table 1 Selected materials. Water
Ethanol
Ethanol
Glycol
Acetone
Glycerol Diesel oil Polystyrene Polyisocyanurate (PIR) Lard
n-butylalcohol Transformer oil PTFE Tin Fat
NaCl solution (wt. 13.6%) No. 11 lubricant Polyethylene foam plastic Paper Skin
NaCl solution (wt. 21.2%) No. 14 lubricant Polyethylene foam ester Glass Muscle
NaCl solution (wt. 29.9%) No. 30 turbine oil Urea foam plastic Cotton Clay
Fig. 3. Structure of the neural network system. Fig. 2. Spectrogram of 1 mm fresh pig tongue section at temperature 15 1C.
2.4. Experimental results of different samples It is shown that the spectrogram of acetone and diesel is similar because there is no difference in their turbidity. For most of the tested liquids, such as transformer oil, lubricant, turbine oil, acetic acid, glycerol, glycerol, acetone, n-butylalcohol and ethanol, they have the same characteristics. But the relations between each other among these spectrograms are different. It is not clear whether the difference of PTFE and fat’s microconstructures accounts for the large variation in the spectrogram of Rd, Td and Tc. Comparing the spectrogram of liquids and solids (Troy and Thennadil, 2001), it is evident that the value of Tc is larger than Td and Rd for the selected liquids. The difference of the values of the measured solids is fairly unremarkable, which is likely due to the turbidity of solid, which is easy to hold up near-infrared. Calculate Rd, Td and Tc of the fresh pig tongue in the dualintegrating sphere experimental system. Fig. 2 shows that the curves of Td and Tc of the pig tongue are similar. But the energy of Rd is lower obviously because of the character of the tongue tissue. For the three curves, the local peak position of Rd agrees well with Td and Tc, whose total energy is of the same order of magnitude. But the energy received by abiotic objects is more. Thus, it is believed that the organism has an effective absorption with near-infrared. Obtaining the optic characteristics of the media is the goal of the experiments. The adding doubling method is employed to solve the nature parameter of optic tissue based on the light distribution in the media. The doubling method assumes knowledge of the reflection and transmission properties for a single thin homogeneous layer. The reflection and transmission of a slab twice as thick is found by juxtaposing two identical slabs and summing the contributions from each slab. The reflection and transmission for an arbitrarily thick slab are obtained by repeatedly doubling until the desired thickness is reached. Inverse adding doubling (IAD), which is the inverse process of AD, was adopted in the calculation. The detailed steps are as follows: first
given a reasonable value of (ma, ms, g); second programmed to calculate the value of ðRd ; T d ; T c Þ Cal ; where the thickness of the section is 1 mm, the temperatures are relatively 10, 15, 20, 25 1C, and the reflecting board whose reflectivity is 0.98 was used as a reference background; third compared the calculated value ðRd ; T d ; T c Þ Cal and the experimental value ðRd ; T d ; T c Þ Exp . If the error between them was larger than the specified value, then a new reasonable value of (ma, ms, g) was given until the error is less than the specified value. Finally, the reasonable value of (ma, ms, g) was seen as the optic characteristics of the media.
3. Black-box model The aim of this paper is to investigate the relationship between the optic parameters and the properties of the organism. This paper focused on analyzing the feasibility of using optic characteristic to investigate the properties of the organism, and simulating the relationship. A new calculation method was derived, in which the properties of the organism were obtained indirectly by a black-box model derived from the nonlinear mapping between the nature parameters of the light and the thermal properties of the organism. 3.1. Neural network model Because the optic parameters and biological thermal properties belong to two different fields, the single-layer neural network cannot reflect their nonlinear relationship. Therefore, the neural network of multiple structures is selected as a black-box model, which can reflect their mutual coupling characteristics. The neural network system (He, 2005) set in this paper has a three-layer structure, as shown in Fig. 3. The first layer is the self-organizing competitive neural network. It is based on the ‘‘lateral inhibition’’ structure in the biological nervous system. The input layer and output layer adopt a two-way link. Their competition layers adopt a horizontal connection. As part of
ARTICLE IN PRESS K. Zhu et al. / Journal of Thermal Biology 34 (2009) 232–236
235
the initial selection, such a structure can simulate the connection of the input variables and target variables possibly. The second layer is the radial basis function network (RBFN), in which the hidden node function responds to the input data. It has a large output resulting in a partial approximate capability, when the input data nears to the central area of the base function. The third layer is the liner neural network. That can classify the vectors into groups that diminish the relative errors effectively. 3.2. Tests of the neural networks One of the key steps of this experiment is to obtain the blackbox model. The tested steps are as follows:
3.3. Evaluation of neural network
Fig. 4. Cross-section structure of fresh pig tongue.
1.0 Thermal Conductivity (W/m K)
(1) Twenty selected samples from 30 objects are divided into four neural networks, because the optical parameters are mapped with the thermal properties of r, Cp, a and n. (2) ma, ms, g are defined as input variables, while r, Cp, a, n as target variables. (3) The self-organizing competitive neural network, the radial basis function network and the linear neural network used Kohonen, hierarchical and LMSE, Widrow–Hoff as their own operational method, respectively. (4) There are four nerve cells in each layer to assure the rationality and the convergence of the results. (5) The input constants a, b, g are set as 1and are multiplied with threshold quantity. It has been proved that the effectiveness of a, b, g is not the function of neural network, and this slims fairly with the threshold quantity in testing changes. (6) In order to confirm that the results agree well with the measured variables, the initial weight values of the three layers are given as 1.5, 1, 0.5, respectively, and the initial threshold values of the three layers are the same as 1. (7) After training, a nonlinear mapping between the optical parameter of the organism and the properties of the organism can be obtained.
0.9 0.8 0.7 0.6 0.5 0.4 0.3 1
In order to evaluate the reliability of this model, the left 10 samples were used as the predicted group to test the model. The results show that the relative errors between the calculated value of the model and the real value were in the range of 5% to 5%, which implied that the model had the ability to predict the thermal properties by the optical parameters.
4. Simulation of neural network 4.1. Experiment materials In biology, a tongue holds a typical organizational fiber structure of muscle, whose thermal parameters are individually different. In order to obtain the exact thermal conductivity, a pig’s tongue was selected as a studied object. In this experiments, 30 fresh pig tongues were tested, whose sketch is shown in Fig. 4. Each tongue was divided into six assigned locations. The slice thickness is 1 mm. Optical parameters were measured in their organizations. 4.2. Simulated results of pig’s tongue and analysis Three simple black-box models are used to predict pig tongue’s
r, Cp, and a with the input of tissue optic parameters, based on which the conductivity of pig’s tongue can be calculated.
2
3
4
5
6
Position of Section
03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Fig. 5. Simulation result of the pig tongue’s thermal conductivity at 20 1C.
The experimental investigation of the thermal conductivity of the pig tongue was conducted with a constant temperature of 20 1C. Fig. 5 shows the comparison of thermal conductivity for 30 pig tongues. From Fig. 5, it can be found that the thermal conductivity varies at different positions, and the average value is 0.68 W/(m K), which is higher than that of skin and muscle. The reviewed data showed that the muscle thermal conductivity is about 0.7 W/(m K) with a temperature of 20 1C, which confirms the reliability of the model. In order to investigate the effects of position and temperature on conductivity, the mean thermal conductivity on different sections with different temperature is shown in Fig. 6. As shown in Fig. 6, the mean conductivities of sections 1, 2 and 3 are higher than that of sections 4, 5 and 6. The results show that the velocity of conducting from the middle to the side of tongue is better than that from the front to the end of the tongue, which results from the typical organizational structure of tongue muscle fiber. The more interesting thing is that the anisotropy feature of the organism had been confirmed by Wang et al. (2007). In Fig. 6, it is also shown that the average thermal conductivities of pig tongue were 0.67, 0.68, 0.68 and 0.68 W(m K) varying with temperatures of 10, 15, 20 and 25 1C, respectively. This implies
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between 5% and 5% compared with the real values, which verified the neural network method’s reliability. The conductivity of the pig tongue was studied by the model and experiments. The results show that the effect of temperature on conductivity of the tongue is not apparent and the ability of conducting from the middle to the side of the tongue is better than that from the front to the end of the tongue, which cannot be measured by the traditional methods.
Thermal Conductivity (W/m K)
0.69 Section 1 Section 2 Section 3 Section 4 Section 5 Section 6
0.68
0.67
Acknowledgment This work is supported by the Project of Chinese National Nature Science Foundation (no. 54076067).
0.66 10°C
15°C
20°C
25°C
Fig. 6. Comparison of mean thermal conductivity for each slice.
that the effect of temperature on conductivity of the tongue is not so apparent.
5. Conclusions Based on the distribution characteristic of the optic radiation energy in the organism under a certain condition, the relationship between the optical parameter of the organism and the properties of the organism was studied, and a new experimental and calculating method was derived, in which the properties of the organism were obtained indirectly by a black-box model derived from the nonlinear mapping between the optical parameter of the organism and the thermal properties of the organism. The model was evaluated by the values of the four thermal properties, such as the density, the constant pressure specific heat, the thermal diffusivity and the viscosity. The results calculated from the black box have an average relative error
References Chia-Wei, Sun, Chih-Yu, Wang, et al., 2001. Polarization gating in ultrafast-optics imaging of skeletal muscle tissues. Opt. Lett. 26 (1), 432–434. Firbank, M., Delpy, D.T., 1993. A design for a stable and reproducible phantom for use in near infrared imaging and spectroscopy. Phys. Med. Bid. 38, 847–853. Han, Y.H., 2003. The research of photon transportation theory in organism tissue and applied in the noninvasive measurement of blood glucose. Master Academic Dissertation, Tianjin University, Tianjin, pp. 25–28. Han, Y.H., 2005. Theories and experiments of measuring the milk composition with near-infrared spectroscopy. Doctor Academic Dissertation, Tianjin University, Tianjin, pp. 33–36. Hatta, I., Sasuga, Y., 1985. Thermal diffusivity measurement of thin films by means of an AC calorimetric method. Rev. Sci. Instrum. 56, 1643–1647. He, J., 2005. Thermal conductivity of organism based on tissue optics method. Master Academic Dissertation, Tianjin University, Tianjin, pp. 35–42. Jackson, W.B., Armer, N.M., et al., 1981. Photothermal deflection spectroscopy and detection. Appl. Opt. 20, 1333–1344. Randall, T.S., 1983. Photoacoustic determination of thin films thermal properties. Appl. Phys. Lett. 42, 955–957. Troy, T.L., Thennadil, S.N., 2001. Optical properties of human skin in the near infrared wavelength range of 1000 to 2200 nm. Journal of Biomedical Optics 6 (2), 167–176. Wang, R.Y., Zhu, K., Chen, R.Q., et al., 2007. Numerical simulation based on finite element method on the 3-D temperature field of the tongue. Journal of Engineering Thermophysics 28, 463–465.
Contents lists available at ScienceDirect
Journal of Thermal Biology journal homepage: www.elsevier.com/locate/jtherbio
A novel method for measuring the thermal conductivity of organisms Kai Zhu, Ya-bo Wang , Ai Yang College of Mechanical Engineering, Tianjin University of Commerce, Tianjin 300134, China
a r t i c l e in f o
a b s t r a c t
Article history: Received 15 October 2008 Accepted 18 February 2009
Based on the theories of tissue optics and artificial neural network, the relationship between the optical properties and biological parameters was studied, and a new experimental method was derived. The properties of the organism were obtained indirectly by a black-box model derived by self-study of the artificial neural network between optical parameters and thermo-physical properties without using the heat transfer equation. In this method, the energy of light in diffuse radiation, diffuse transmission and collimated transmission was absorbed by a dual-integrating sphere experimental system of a spectrometer, and the spectrogram of the energy was obtained. Combining these spectral data of the energy, the diffuse-reflecting power, the diffuse transmissivity and the collimated transmissivity were calculated. The calculated results were taken as the input parameters of a black-box model. The experimental results show that there are apparent differences between the spectrogram of the energy on the diffuse radiation, the diffuse transmission and the collimated transmission of different matters, while there is a little difference in the same matter. Each spectrogram has its own characteristic. The values of the four thermal properties including the density, the constant pressure specific heat, the thermal diffusivity and the viscosity were calculated using the black-box model. Compared with the real values the calculated one has an average relative error between 5% and 5%. The conductivity of the tongue is 0.68 W/(m K) that calculated from the value of the density, the constant pressure specific heat and the thermal diffusivity. The results also show that there is a little difference on the conductivities in the longitudinal cross-section and the transverse section, but the effect of temperature on the conductivity of the tongue is not apparent. The difference implies the anisotropy of the properties of the organism, which cannot be easily obtained by a conventional experimental method. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Properties Bio-heat transfer Bio-optics Artificial neural network
1. Introduction Because of the complex structures with blood circulation, the thermal properties of the organism are different from those of inert materials, which vary with their type, structure and temperature. Therefore, the precise measurement of thermal properties in a biological tissue has become an important part of the study in biological technology. The aim of this paper is to study the relationship between the optical parameters and the biological properties, which are based on the distribution characteristic of optic radiation energy in the organism under a special condition. There are some reports about the application of optical theories in the study of thermal conductivity (Chia-Wei et al., 2001; Hatta and Sasuga, 1985; He, 2005). It was found in some turbid substances, such as polystyrene, milk or blood, that their characteristics of absorption and scattering are relatively stable. This is similar to the optical properties of organisms (Jackson et al., 1981; Han, 2003, 2005; Firbank and Delpy, 1993; Randall,
Corresponding author. Tel: +86 13512014043.
E-mail address: [email protected] (Y.-b. Wang). 0306-4565/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jtherbio.2009.02.007
1983). Based on this, the transferring rules and characteristics of light in organisms were studied to find the relationship between the nature parameters of the light and the properties of the organism. The optical parameters are used to describe the interaction between the optic, and the media is used to embody the micro-characteristics of materials. The complex interaction between light and organism tissue can be summed up as thermal effects, mechanical effects, photochemical effects, electromagnetic fields effect and biological effects. In this paper, the proposed method to simulate the distributing characteristics of light in organism tissues is based on determining the nature parameters such as the absorption coefficient, scattering coefficient and anisotropic factor with the analytic theory and the numerical theory. Compared with the traditional method, there are some advantages to the proposed method:
(1) The proposed method is fit for the materials with different structure and bioactivity such as organic tissues whilst the traditional methods are used to measure inert materials. (2) Instead of adopting the conventional heat transfer equation, the proposed method is used to obtain the optical parameters
ARTICLE IN PRESS K. Zhu et al. / Journal of Thermal Biology 34 (2009) 232–236
Nomenclature
a Cp Icr Ics Irr
Irs Itr
Its Rd Rdr Tcr Tdr Tc Td
thermal diffusivity, m2/s constant pressure specific heat, J/(kg K) energy of light received by detector 3, due to air contact with a dual-integrating sphere, W/m2 energy of light received by detector 3, due to sample contact with a dual-integrating sphere, W/m2 energy of light received by detector 1, due to standard reflective board contact with a dual-integrating sphere, W/m2 energy of light received by detector 1, due to sample contact with a dual-integrating sphere, W/m2 energy of light received by detector 2, due to standard reflective board posted to contact the second integrated sphere, W/m2 energy of light received by detector 2, due to sample contact with a dual-integrating sphere, W/m2 total diffuse reflectance diffuse reflectance of standard reflective board collimated transmittance of air diffuse transmittance of air total collimated transmittance total diffuse transmittance
233
Greek symbols
a, b, g
empirical constant
Empirical constant
l
ma ms n r g
mean thermal conductivity, W m1 K1 absorption coefficient, m2/s dissipation coefficient, m2/s viscosity, Pa s density, kg/m3 anisotropy factor
Subscripts a c cal d exp eq fig s
air, absorption coefficient collimated transmittance calculated diffuse reflectance, diffuse transmittance experimental equation figure sample, scatter coefficient
of organisms by a black-box model from the nonlinear mapping between the nature parameters of light and the thermal properties of the organism. (3) The proposed method does not require detailed knowledge of the mechanism.
of error during the process, an extinction long tube and an attenuating medium were applied in the experiment. When measuring, some parameters such as the total diffuse reflectance Rd, total diffuse transmittance Td, and the total collimated transmittance Tc can be obtained as follows (symbols not consistent with equations):
2. Optic experiments of tissues
Rd ¼
Irs R Irr ds
(1)
Td ¼
Its T Itr dr
(2)
Tc ¼
Ics T cr Icr
(3)
2.1. Measuring system The schematic (Han, 2003) of the dual-integrating sphere experimental system of the spectrometer is shown in Fig. 1. As shown in the figure, the tested object was arranged between the dual-integrating spheres. The near-infrared light emitted by FT-IR spectroscopy irradiates to the dual-integrating spheres through reflector plate and lens. Schematic of the dual-integrating sphere experimental system of spectrometer diffuse radiation, diffuse transmission and the collimated transmission of the tested object were received by InGaAs detectors 1, 2 and 3, respectively. Then the spectrogram of the energy was obtained by a computer connected to the experimental system. To apply the ‘‘Adding Double’’ to the experiment, it is necessary to determine the entrance direction vertically to the measured object. In addition, the size of spot on the tested material caused by the light is less than 10% of the integral sphere window filed. To reduce the effect
It is necessary to determine Rd, Td and Tc first. They are the foundation of calculating thermal properties. 2.2. Preparation of experimental materials In order to get the measured parameters, 30 samples were selected and are shown in Table 1. Because these samples were used as a reference, their relative parameters were known to verify the reliability and rationality of the nonlinear mapping between the nature parameters of the light and the thermal properties of the organism. In addition, to characterize the thermal performance of solid objects, it is necessary to determine the light transmittance of sliced materials. 2.3. Experimental design
Fig. 1. The dual-integrating sphere experimental system of the spectrometer.
Rd, Td, Tc given by Eqs. (1)–(3) are the input data to the blackbox model, and the computation of these parameters usually involves a tedious mathematical process, which requires the determination of the spectrogram of the energy in a dualintegrating sphere experimental system of a spectrometer. In order to obtain the correct value, the test is iterated by using the above selected objects.
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Table 1 Selected materials. Water
Ethanol
Ethanol
Glycol
Acetone
Glycerol Diesel oil Polystyrene Polyisocyanurate (PIR) Lard
n-butylalcohol Transformer oil PTFE Tin Fat
NaCl solution (wt. 13.6%) No. 11 lubricant Polyethylene foam plastic Paper Skin
NaCl solution (wt. 21.2%) No. 14 lubricant Polyethylene foam ester Glass Muscle
NaCl solution (wt. 29.9%) No. 30 turbine oil Urea foam plastic Cotton Clay
Fig. 3. Structure of the neural network system. Fig. 2. Spectrogram of 1 mm fresh pig tongue section at temperature 15 1C.
2.4. Experimental results of different samples It is shown that the spectrogram of acetone and diesel is similar because there is no difference in their turbidity. For most of the tested liquids, such as transformer oil, lubricant, turbine oil, acetic acid, glycerol, glycerol, acetone, n-butylalcohol and ethanol, they have the same characteristics. But the relations between each other among these spectrograms are different. It is not clear whether the difference of PTFE and fat’s microconstructures accounts for the large variation in the spectrogram of Rd, Td and Tc. Comparing the spectrogram of liquids and solids (Troy and Thennadil, 2001), it is evident that the value of Tc is larger than Td and Rd for the selected liquids. The difference of the values of the measured solids is fairly unremarkable, which is likely due to the turbidity of solid, which is easy to hold up near-infrared. Calculate Rd, Td and Tc of the fresh pig tongue in the dualintegrating sphere experimental system. Fig. 2 shows that the curves of Td and Tc of the pig tongue are similar. But the energy of Rd is lower obviously because of the character of the tongue tissue. For the three curves, the local peak position of Rd agrees well with Td and Tc, whose total energy is of the same order of magnitude. But the energy received by abiotic objects is more. Thus, it is believed that the organism has an effective absorption with near-infrared. Obtaining the optic characteristics of the media is the goal of the experiments. The adding doubling method is employed to solve the nature parameter of optic tissue based on the light distribution in the media. The doubling method assumes knowledge of the reflection and transmission properties for a single thin homogeneous layer. The reflection and transmission of a slab twice as thick is found by juxtaposing two identical slabs and summing the contributions from each slab. The reflection and transmission for an arbitrarily thick slab are obtained by repeatedly doubling until the desired thickness is reached. Inverse adding doubling (IAD), which is the inverse process of AD, was adopted in the calculation. The detailed steps are as follows: first
given a reasonable value of (ma, ms, g); second programmed to calculate the value of ðRd ; T d ; T c Þ Cal ; where the thickness of the section is 1 mm, the temperatures are relatively 10, 15, 20, 25 1C, and the reflecting board whose reflectivity is 0.98 was used as a reference background; third compared the calculated value ðRd ; T d ; T c Þ Cal and the experimental value ðRd ; T d ; T c Þ Exp . If the error between them was larger than the specified value, then a new reasonable value of (ma, ms, g) was given until the error is less than the specified value. Finally, the reasonable value of (ma, ms, g) was seen as the optic characteristics of the media.
3. Black-box model The aim of this paper is to investigate the relationship between the optic parameters and the properties of the organism. This paper focused on analyzing the feasibility of using optic characteristic to investigate the properties of the organism, and simulating the relationship. A new calculation method was derived, in which the properties of the organism were obtained indirectly by a black-box model derived from the nonlinear mapping between the nature parameters of the light and the thermal properties of the organism. 3.1. Neural network model Because the optic parameters and biological thermal properties belong to two different fields, the single-layer neural network cannot reflect their nonlinear relationship. Therefore, the neural network of multiple structures is selected as a black-box model, which can reflect their mutual coupling characteristics. The neural network system (He, 2005) set in this paper has a three-layer structure, as shown in Fig. 3. The first layer is the self-organizing competitive neural network. It is based on the ‘‘lateral inhibition’’ structure in the biological nervous system. The input layer and output layer adopt a two-way link. Their competition layers adopt a horizontal connection. As part of
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235
the initial selection, such a structure can simulate the connection of the input variables and target variables possibly. The second layer is the radial basis function network (RBFN), in which the hidden node function responds to the input data. It has a large output resulting in a partial approximate capability, when the input data nears to the central area of the base function. The third layer is the liner neural network. That can classify the vectors into groups that diminish the relative errors effectively. 3.2. Tests of the neural networks One of the key steps of this experiment is to obtain the blackbox model. The tested steps are as follows:
3.3. Evaluation of neural network
Fig. 4. Cross-section structure of fresh pig tongue.
1.0 Thermal Conductivity (W/m K)
(1) Twenty selected samples from 30 objects are divided into four neural networks, because the optical parameters are mapped with the thermal properties of r, Cp, a and n. (2) ma, ms, g are defined as input variables, while r, Cp, a, n as target variables. (3) The self-organizing competitive neural network, the radial basis function network and the linear neural network used Kohonen, hierarchical and LMSE, Widrow–Hoff as their own operational method, respectively. (4) There are four nerve cells in each layer to assure the rationality and the convergence of the results. (5) The input constants a, b, g are set as 1and are multiplied with threshold quantity. It has been proved that the effectiveness of a, b, g is not the function of neural network, and this slims fairly with the threshold quantity in testing changes. (6) In order to confirm that the results agree well with the measured variables, the initial weight values of the three layers are given as 1.5, 1, 0.5, respectively, and the initial threshold values of the three layers are the same as 1. (7) After training, a nonlinear mapping between the optical parameter of the organism and the properties of the organism can be obtained.
0.9 0.8 0.7 0.6 0.5 0.4 0.3 1
In order to evaluate the reliability of this model, the left 10 samples were used as the predicted group to test the model. The results show that the relative errors between the calculated value of the model and the real value were in the range of 5% to 5%, which implied that the model had the ability to predict the thermal properties by the optical parameters.
4. Simulation of neural network 4.1. Experiment materials In biology, a tongue holds a typical organizational fiber structure of muscle, whose thermal parameters are individually different. In order to obtain the exact thermal conductivity, a pig’s tongue was selected as a studied object. In this experiments, 30 fresh pig tongues were tested, whose sketch is shown in Fig. 4. Each tongue was divided into six assigned locations. The slice thickness is 1 mm. Optical parameters were measured in their organizations. 4.2. Simulated results of pig’s tongue and analysis Three simple black-box models are used to predict pig tongue’s
r, Cp, and a with the input of tissue optic parameters, based on which the conductivity of pig’s tongue can be calculated.
2
3
4
5
6
Position of Section
03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Fig. 5. Simulation result of the pig tongue’s thermal conductivity at 20 1C.
The experimental investigation of the thermal conductivity of the pig tongue was conducted with a constant temperature of 20 1C. Fig. 5 shows the comparison of thermal conductivity for 30 pig tongues. From Fig. 5, it can be found that the thermal conductivity varies at different positions, and the average value is 0.68 W/(m K), which is higher than that of skin and muscle. The reviewed data showed that the muscle thermal conductivity is about 0.7 W/(m K) with a temperature of 20 1C, which confirms the reliability of the model. In order to investigate the effects of position and temperature on conductivity, the mean thermal conductivity on different sections with different temperature is shown in Fig. 6. As shown in Fig. 6, the mean conductivities of sections 1, 2 and 3 are higher than that of sections 4, 5 and 6. The results show that the velocity of conducting from the middle to the side of tongue is better than that from the front to the end of the tongue, which results from the typical organizational structure of tongue muscle fiber. The more interesting thing is that the anisotropy feature of the organism had been confirmed by Wang et al. (2007). In Fig. 6, it is also shown that the average thermal conductivities of pig tongue were 0.67, 0.68, 0.68 and 0.68 W(m K) varying with temperatures of 10, 15, 20 and 25 1C, respectively. This implies
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between 5% and 5% compared with the real values, which verified the neural network method’s reliability. The conductivity of the pig tongue was studied by the model and experiments. The results show that the effect of temperature on conductivity of the tongue is not apparent and the ability of conducting from the middle to the side of the tongue is better than that from the front to the end of the tongue, which cannot be measured by the traditional methods.
Thermal Conductivity (W/m K)
0.69 Section 1 Section 2 Section 3 Section 4 Section 5 Section 6
0.68
0.67
Acknowledgment This work is supported by the Project of Chinese National Nature Science Foundation (no. 54076067).
0.66 10°C
15°C
20°C
25°C
Fig. 6. Comparison of mean thermal conductivity for each slice.
that the effect of temperature on conductivity of the tongue is not so apparent.
5. Conclusions Based on the distribution characteristic of the optic radiation energy in the organism under a certain condition, the relationship between the optical parameter of the organism and the properties of the organism was studied, and a new experimental and calculating method was derived, in which the properties of the organism were obtained indirectly by a black-box model derived from the nonlinear mapping between the optical parameter of the organism and the thermal properties of the organism. The model was evaluated by the values of the four thermal properties, such as the density, the constant pressure specific heat, the thermal diffusivity and the viscosity. The results calculated from the black box have an average relative error
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